Horndeski extension of the minimal theory of quasidilaton massive gravity

Abstract

The minimal theory of quasidilaton massive gravity allows for a stable self-accelerating de Sitter solution in a wide range of parameters. On the other hand, in order for the theory to be compatible with local gravity tests, the fifth force due to the quasidilaton scalar needs to be screened at local scales. The present paper thus extends the theory by inclusion of a cubic Horndeski term in a way that (i) respects the quasidilaton global symmetry, that (ii) maintains the physical degrees of freedom in the theory being three, that (iii) can accommodate the Vainshtein screening mechanism and that still (iv) allows for a stable self-accelerating de Sitter solution. After adding the Horndeski term (and a k-essence type nonlinear kinetic term as well) to the precursor action, we switch to the Hamiltonian language and find a complete set of independent constraints. We then construct the minimal theory with three physical degrees of freedom by carefully adding a pair of constraints to the total Hamiltonian of the precursor theory. Switching back to the Lagrangian language, we study cosmological solutions and their stability in the minimal theory. In particular, we show that a self-accelerating de Sitter solution is stable for a wide range of parameters. Furthermore, as in the minimal theory of massive gravity, the propagation speed of the massive gravitational waves in the high momentum limit precisely agrees with the speed of light.

Phenomenology of minimal theory of quasidilaton massive gravity

“…In this work, we study both background cosmology and linear perturbations in the presence of matter fields, thus extending the work done in [18]. We show that the dynamics of the quasidilaton scalar allow for an attractor that generalizes the attractor present in vacuum to the system with matter, analyze inhomogeneous perturbations around this attractor solution in the presence of matter, derive the stability conditions and find the expression for the effective gravitational constant in the quasistatic approximation.…”

“…It thus propagates only three degrees of freedom, two tensors as in GR and the quasidilaton scalar, and can accommodate the Vainshtein screening for the quasidilaton. Therefore its phenomenology remains close to general relativity while giving a small mass (of cosmological value) to gravitational waves.In this work, we study both background cosmology and linear perturbations in the presence of matter fields, thus extending the work done in [18]. We show that the dynamics of the quasidilaton scalar allow for an attractor that generalizes the attractor present in vacuum to the system with matter, analyze inhomogeneous perturbations around this attractor solution in the presence of matter, derive the stability conditions and find the expression for the effective gravitational constant in the quasistatic approximation.The paper is organized as follows: in section II we present the complete action for the minimal theory of quasidilaton massive gravity, in the unitary gauge.…”

“…Building upon [18] 1 , the action for the minimal quasidilaton, in the presence of matter, may be written using the objects defined above as…”

“…whereS EH is a part that includes the Einstein-Hilbert action for the physical metric g µν (without cosmological constant, since this one is included in the graviton mass term),S σ is a part that includes the kinetic term of the quasidilaton scalar field σ, S pot is the precursor graviton mass term, S C is a part that includes the additional constraints which remove the scalar graviton mode, and S m is the matter action. For compactness, both kinetic terms for the graviton and the quasidilaton may be supplemented by a contribution from the quasidilaton cubic Horndeski sector, whose tertiary constraint mixes with the supplementary constraints used to minimize the number of physical degrees of freedom in the theory [18]. We thus rewrite the action in a way that includes these contributions into the kinetic terms, i.e.…”

“…In order to evade the practical issues, several extensions of dRGT massive gravity have thus since then been proposed, for instance: massive bigravity [5], mass-varying massive gravity [6], modified matter couplings [7], scalar field extensions [8][9][10][11][12], and Lorentz symmetry violating extensions [13][14][15][16]. This has proven to be a fruitful path: several of these extensions are healthy and lead to interesting, non-Λ cold dark matter (non-ΛCDM) phenomenology.The minimal theory of quasidilaton massive gravity [17,18], by means of a weak violation of Lorentz invariance and the addition of a scalar field called the quasidilaton, has been shown i) to provide a stable cosmological vacuum de Sitter solution corresponding to a late-time de Sitter attractor, and ii) to accommodate the Vainshtein mechanism [19] to screen fifth force effects via a Horndeski-type kinetic term [20] for the quasidilaton field. On a similar basis as the minimal theory of massive gravity (MTMG) [13], the theory possesses constraints that remove the graviton scalar and vector modes.…”